pH-Dependent Structure and Dynamics of the Catalytic Domains of Human Carbonic Anhydrase II and IX.

Extensive computer simulation studies have been carried out to probe the pH-dependent structure and dynamics of the two most efficient isoenzymes II and IX of human carbonic anhydrase (HCA) that control the pH in the human body. The equilibrium structure and hydration of their catalytic domains are found to be largely unaffected by the variation of pH in the range studied, in close agreement with the known experimental results. In contrast, a significant effect of the change in pH is observed for the first time on the local electrostatic potential of the active site walls and the dynamics of active site water molecules. We also report for the first time the free energy and kinetics of coupled fluctuations of orientation and protonation states of the well-known His-mediated proton shuttle (His-64) in both isozymes at pH 7 and 8. The transitions between different tautomers of in or out conformations of His-64 side chain range between 109 and 106 s-1 depending on pH. Possible implications of these results on conformation-dependent pKa of His-64 side chain and its role in driving the catalysis toward hydration of CO2 or dehydration of HCO3- with varying pH are discussed.

A Case Study on the Use of Binding Free Energies to Screen Inhibitors of Human Carbonic Anhydrase II.

We present in this article a case study on the thermodynamics of binding to human carbonic anhydrase II (HCA II) by three well-known inhibitors, viz. (a) acetazolamide (AZM) that directly binds to the catalytic Zn(II) ion at the active site, (b) non-zinc binding 6-hydroxy-2-thioxocoumarin (FC5) (c) 2-[(S)-benzylsulfinyl]benzoic acid (3G1). In each case, the crystal structure or its analogue of inhibitor-bound HCA II has been used to perform classical molecular dynamics (MD) simulation in water till 1 µ s ${1\hskip0.33em\mu s}$ . AZM and FC5 are found to undergo repeated binding and unbinding with markedly different dynamics from the partially buried, substrate-binding hydrophobic pocket near the active site. 3G1, on the other hand, is found to remain mostly at its crystallographic binding site occluded from the active site of HCA II. The associated binding free energies ( Δ G b i n d , s o l v ${{\rm \Delta }{G}_{bind,solv}}$ ) have been computed using the known MM/GBSA method and compared to the available experimental data. Our results show that Δ G b i n d , s o l v ${{\rm \Delta }{G}_{bind,solv}}$ encounters several issues including limited sampling of multiple binding sites and incorrect prediction of the affinity of the chosen ligands. Possible use of the simulation results in further construction of Markov state models is also discussed.

In the footsteps of an inhibitor unbinding from the active site of human carbonic anhydrase II.

The crystal structure of human carbonic anhydrase (HCA) II bound to an inhibitor molecule, 6-hydroxy-2-thioxocoumarin (FC5), shows FC5 to be located in a hydrophobic pocket at the active site. The present work employs classical molecular dynamics (MD) simulation to follow the FC5 molecule for 1 µs as it unbinds from its binding location, adopts the path of substrate/product diffusion (path 1) to leave the active site at around 75 ns. It is then found to undergo repeated binding and unbinding at different locations on the surface of the enzyme in water. Several transient excursions through different regions of the enzyme are also observed prior to its exit from the active site. These transient paths are combined with functionally relevant cavities/channels to enlist five additional pathways (path 2-6). Pathways 1-6 are subsequently explored using steered MD and umbrella sampling simulations. A free energy barrier of 0.969 kcal mol-1 is encountered along path 1, while barriers in the range of 0.57-2.84 kcal mol-1 are obtained along paths 2, 4 and 5. We also analyze in detail the interaction between FC5 and the enzyme along each path as the former leaves the active site of HCA II. Our results indicate path 1 to be the major exit pathway for FC5, although competing contributions may also come from the paths 2, 4 and 5.Communicated by Ramaswamy H. Sarma.

Structure and Dynamics of the Isozymes II and IX of Human Carbonic Anhydrase.

Human carbonic anhydrases (HCAs) are responsible for the pH control and sensing in our body and constitute key components in the central pH paradigm connected to cancer therapeutics. However, little or no molecular level studies are available on the pH-dependent stability and functional dynamics of the known isozymes of HCA. The main objective of this Article is to report the first bench-marking study on the structure and dynamics of the two most efficient isozymes, HCA II and IX, at neutral pH using classical molecular dynamics (MD) and constant pH MD (CpHMD) simulations combined with umbrella sampling, transition path sampling, and Markov state models. Starting from the known crystal structures of HCA II and the monomeric catalytic domain of HCA IX (labeled as HCA IX-c), we have generated classical MD and CpHMD trajectories (of length 1 µs each). In all cases, the overall stability, RMSD, and secondary structure segments of the two isozymes are found to be quite similar. Functionally important dynamics of these two enzymes have been probed in terms of active site hydration, coordination of the Zn(II) ion to a transient excess water, and the formation of putative proton transfer paths. The most important difference between the two isozymes is observed for the side-chain fluctuations of His-64 that is expected to shuttle an excess proton out of the active site as a part of the rate-determining intramolecular proton transfer reaction. The relative stability of the stable inward and outward conformations of the His-64 side-chain and the underlying free energy surfaces are found to depend strongly on the isozyme. In each case, a lower free energy barrier is detected between predominantly inward conformations from predominantly outward ones when simulated under constant pH conditions. The kinetic rate constants of interconversion between different free energy basins are found to span 107-108 s-1 with faster conformational transitions predicted at constant pH condition. The estimated rate constants and free energies are expected to validate if the fluctuation of the His-64 side-chain in HCA IX may have a significance similar to that known in the multistep catalytic cycle of HCA II.

Nonlinear Reaction Coordinate of an Enzyme Catalyzed Proton Transfer Reaction.

We present an in-depth study on the theoretical calculation of an optimum reaction coordinate as a linear or nonlinear combination of important collective variables (CVs) sampled from an ensemble of reactive transition paths for an intramolecular proton transfer reaction catalyzed by the enzyme human carbonic anhydrase (HCA) II. The linear models are optimized by likelihood maximization for a given number of CVs. The nonlinear models are based on an artificial neural network with the same number of CVs and optimized by minimizing the root-mean-square error in comparison to a training set of committor estimators generated for the given transition. The nonlinear reaction coordinate thus obtained yields the free energy of activation and rate constant as 9.46 kcal mol-1 and 1.25 × 106 s-1, respectively. These estimates are found to be in quantitative agreement with the known experimental results. We have also used an extended autoencoder model to show that a similar analysis can be carried out using a single CV only. The resultant free energies and kinetics of the reaction slightly overestimate the experimental data. The implications of these results are discussed using a detailed microkinetic scheme of the proton transfer reaction catalyzed by HCA II.

Coordination Dynamics of Zinc Triggers the Rate Determining Proton Transfer in Human Carbonic Anhydrase II.

We present, for the first time, how transient changes in the coordination number of zinc ion affects the rate determining step in the enzyme human carbonic anhydrase (HCA) II. The latter involves an intramolecular proton transfer between a zinc-bound water and a distant histidine residue (His-64). In the absence of time-resolved experiments, results from classical and QM-MM molecular dynamics and transition path sampling simulations are presented. The catalytic zinc ion is found to be present in two possible coordination states; viz. a stable tetra-coordinated state, T and a less stable penta-coordinated state, P with tetrahedral and trigonal bipyramidal coordination geometries, respectively. A fast dynamical inter-conversion occurs between T and P due to reorganization of active site water molecules making the zinc ion more positively charged in state P. When initiated from different coordination environments, the most probable mechanism of proton transfer is found to be deprotonation of the equatorial water molecule from state P and transfer of the excess proton via a short path formed by hydrogen bonded network of active site water molecules. We estimate the rate constant of proton transfer as kP=1.29×106s-1 from P and kT=4.37×104s-1 from T. A quantitative match of estimated kP with the experimental value, ( kexp∼0.8×106s-1 ) suggests that dynamics of Zn coordination triggers the rate determining proton transfer step in HCA II.

Orthogonal order parameters to model the reaction coordinate of an enzyme catalyzed reaction.

The choice of suitable collective variables in formulating an optimal reaction coordinate is a challenging task for activated transitions between a pair of stable states especially when dealing with biochemical changes such as enzyme catalyzed reactions. A detailed benchmarking study is carried out on the choice of collective variables that can distinguish between the stable states unambiguously. We specifically address the issue if these variables may be directly used to model the optimal reaction coordinate, or if it would be better to use their orthogonalized counterparts. The proposed computational scheme is applied to the rate determining intramolecular proton transfer step in the enzyme human carbonic anhydrase II. The optimum reaction coordinate is determined with and without orthogonalization of the collective variables pertinent to a key conformational fluctuation and the actual proton transfer step at the active site of the enzyme. Suitability of the predicted reaction coordinates in different processes is examined in terms of the free energy profile projected along the reaction coordinate, the rate constant of transition and the underlying molecular mechanism of barrier crossing. Our results indicate that a better agreement with earlier simulation and experimental data is obtained when the orthogonalized collective variables are used to model the reaction coordinate.

Reaction Coordinate, Free Energy, and Rate of Intramolecular Proton Transfer in Human Carbonic Anhydrase II.

The role of structure and dynamics of an enzyme has been investigated at three different stages of its function including the chemical event it catalyzes. A one-pot computational method has been designed for each of these stages on the basis of classical and/or quantum mechanical-molecular mechanical molecular dynamics and transition path sampling simulations. For a pair of initial and final states A and B separated by a high free-energy barrier, using a two-stage selection process, several collective variables (CVs) are identified that can delineate A and B. However, these CVs are found to exhibit strong cross-coupling over the transition paths. A set of mutually orthogonal order parameters is then derived from these CVs and an optimal reaction coordinate, r, determined applying half-trajectory likelihood maximization along with a Bayesian information criterion. The transition paths are also used to project the multidimensional free energy surface and barrier crossing dynamics along r. The proposed scheme has been applied to the rate-determining intramolecular proton transfer reaction of the well-known enzyme human carbonic anhydrase II. The potential of mean force, F( r), in the absence of the chemical step is found to reproduce earlier results on the equilibrium population of two side-chain orientations of key residue His-64. Estimation of rate constants, k, from mean first passage times for the three different stages of catalysis shows that the rate-determining step of intramolecular proton transfer occurs with k ≃ 1.0 × 106 s-1, in close agreement with known experimental results.

Coupling Protein Dynamics with Proton Transport in Human Carbonic Anhydrase II.

The role of protein dynamics in enzyme catalysis is one of the most highly debated topics in enzymology. The main controversy centers around what may be defined as functionally significant conformational fluctuations and how, if at all, these fluctuations couple to enzyme catalyzed events. To shed light on this debate, the conformational dynamics along the transition path surmounting the highest free energy barrier have been herein investigated for the rate limiting proton transport event in human carbonic anhydrase (HCA) II. Special attention has been placed on whether the motion of an excess proton is correlated with fluctuations in the surrounding protein and solvent matrix, which may be rare on the picosecond and subpicosecond time scales of molecular motions. It is found that several active site residues, which do not directly participate in the proton transport event, have a significant impact on the dynamics of the excess proton. These secondary participants are shown to strongly influence the active site environment, resulting in the creation of water clusters that are conducive to fast, moderately slow, or slow proton transport events. The identification and characterization of these secondary participants illuminates the role of protein dynamics in the catalytic efficiency of HCA II.

Identification of putative unfolding intermediates of the mutant His-107-tyr of human carbonic anhydrase II in a multidimensional property space.

In this article, we develop an extensive search procedure of the multi-dimensional folding energy landscape of a protein. Our aim is to identify different classes of structures that have different aggregation propensities and catalytic activity. Following earlier studies by Daggett et al. [Jong, D. D.; Riley, R.: Alonso, D.O.: Dagett, V. J. Mol. Biol. 2002, 319, 229], a series of high temperature all-atom classical molecular simulation studies has been carried out to derive a multi-dimensional property space. Dynamical changes in these properties are then monitored by projecting them along a one-dimensional reaction coordinate, dmean . We have focused on the application of this method to partition a wide array of conformations of wild type human carbonic anhydrase II (HCA II) and its unstable mutant His-107-Tyr along dmean by sampling a 35-dimensional property space. The resultant partitioning not only reveals the distribution of conformations corresponding to stable structures of HCA II and its mutant, but also allows the monitoring of several partially unfolded and less stable conformations of the mutant. We have investigated the population of these conformations at different stages of unfolding and collected separate sets of structures that are widely separated in the property space. The dynamical diversity of these sets are examined in terms of the loading of their respective first principal component. The partially unfolded structures thus collected are qualitatively mapped on to the experimentally postulated light molten globule (MGL) and molten globule (MG) intermediates with distinct aggregation propensities and catalytic activities. Proteins 2016; 84:726-743. © 2016 Wiley Periodicals, Inc.

Determination of the Reaction Coordinate for a Key Conformational Fluctuation in Human Carbonic Anhydrase II.

During the reversible hydration of carbon dioxide into bicarbonate by the enzyme human carbonic anhydrase II, the rate-determining step of proton transfer across the active site has been suggested to involve side chain rotation of the residue His-64 shuttling an excess proton in and out of the active site. In the present article, we have determined the reaction coordinate for this catalytically important conformational transition starting from a set of 32 order parameters (or candidate collective variables). Following the original work by Peters and Trout (J. Chem. Phys. 2006, 125, 054108), unbiased dynamical transition paths connecting the two major side chain conformations are harvested using an aimless shooting algorithm, and the reaction coordinate is determined using the method of forward-trajectory likelihood maximization. Several different models are tested involving a single order parameter or linear combinations of several of them chosen from the preselected set. An optimum reaction coordinate, identified using a Bayesian information criterion, is found to be a linear combination of 4 order parameters. This reaction coordinate is subsequently utilized to explore the associated free energy profile and diffusive barrier crossing dynamics. To the best of our knowledge, previous instances of this calculation include only alanine dipeptide and photoactive yellow protein (125 residues) in explicit water solvent. The present work is the first report of a quantitative determination of the reaction coordinate for conformational transition in a protein having as many as 259 residues in the presence of explicit water and sampled near the free energy barrier for about 1 µs.

Structure and dynamics of water inside endohedrally functionalized carbon nanotubes.

We have carried out classical molecular dynamics simulations on the formation of extended water chains inside single-walled carbon nanotubes (SWCNTs) in water in the presence of selected functional groups covalently attached to the inner wall of the tube. Analogues of polar amino acid sidechains have been chosen to carry out the endohedral functionalization of SWCNTs. Our results show a spontaneous and asymmetric filling of the nanotube with dynamical water chains in all the cases studied. The presence of Asp- and Glu-like sidechains is found to result in the formation of well-ordered water chains across the tube having the maximum number of water molecules being retained within the core with the largest residence times. The presence of methyl or methylene groups along the suspended chain is observed to disrupt the formation of water chains with higher length and/or longer residence times. The importance of hydrogen bonding in forming these water chains is assessed in terms of the relaxations of different hydrogen bond correlation functions. For a given dimension of the hydrophobic nanopore, we thus obtain a scale comparing the ability of carboxylic, alcohol, and imidazole groups in controlling the structure and dynamics of water in it. Our results also suggest that SWCNTs of varying lengths, endohedrally functionalized with Asp- and Glu-like sidechains, may be used as design templates in CNT-based water storage devices.

Modeling the structure and proton transfer pathways of the mutant His-107-Tyr of human carbonic anhydrase II.

We present molecular modeling of the structure and possible proton transfer pathways from the surface of the protein to the zinc-bound water molecule in the active site of the mutant His-107-Tyr of human carbonic anhydrase II (HCAII). No high-resolution structure or crystal structure is available till now for this particular mutant due to its lack of stability at physiological temperature. Our analysis utilizes as starting point a series of structures derived from high-resolution crystal structure of the wild type protein. While many of the structures investigated do not reveal a complete path between the zinc bound water and His-64, several others do indicate the presence of a transient connection even when His-64 is present in its outward conformation. Mutation at the residue 107 also reveals the formation of a new path into the active site. Competing contributions from His-64 sidechain rotation from its outward conformation are also evaluated in terms of optimal path analysis. No indication of a lower catalytic efficiency of the mutant is evident from our results under the condition of thermal stability of the mutant.

Chemical rescue of enzymes: proton transfer in mutants of human carbonic anhydrase II.

In human carbonic anhydrase II (HCA II), the mutation of position 64 from histidine to alanine (H64A) disrupts the rate limiting proton transfer (PT) event, resulting in a reduction of the catalytic activity of the enzyme as compared to the wild-type. Potential of mean force (PMF) calculations utilizing the multistate empirical valence bond (MS-EVB) methodology for H64A HCA II yields a PT free energy barrier significantly higher than that found in the wild-type enzyme. This high barrier, determined in the absence of exogenous buffer and assuming no additional ionizable residues in the PT pathway, indicates the likelihood of alternate enzyme pathways that utilize either ionizable enzyme residues (self-rescue) and/or exogenous buffers (chemical rescue). It has been shown experimentally that the catalytic activity of H64A HCA II can be chemically rescued to near wild-type levels by the addition of the exogenous buffer 4-methylimidazole (4MI). Crystallographic studies have identified two 4MI binding sites, yet site-specific mutations intended to disrupt 4MI binding have demonstrated these sites to be nonproductive. In the present work, MS-EVB simulations show that binding of 4MI near Thr199 in the H64A HCA II mutant, a binding site determined by NMR spectroscopy, results in a viable chemical rescue pathway. Additional viable rescue pathways are also identified where 4MI acts as a proton transport intermediary from the active site to ionizable residues on the rim of the active site, revealing a probable mode of action for the chemical rescue pathway.

Role of protein motions on proton transfer pathways in human carbonic anhydrase II.

We report here a theoretical study on the formation of long-range proton transfer pathways in proteins due to side chain conformational fluctuations of amino acid residues and reorganization of interior hydration positions. The proton transfer pathways in such systems may be modeled as fluctuating hydrogen-bonded networks with both short- and long-lived connections between the networked nodes, the latter being formed by polar protein atoms and water molecules. It is known that these fluctuations may extend over several decades of time ranging from a few femtoseconds to a few milliseconds. We have shown in this article how the use of a variety of theoretical methods may be utilized to detect a generic set of pathways and assess the feasibility of forming one or more transient connections. We demonstrate the application of these methods to the enzyme human carbonic anhydrase II and its mutants. Our results reveal several alternative pathways in addition to the one mediated by His-64. We also probe at length the mechanism of key conformational fluctuations contributing to the formation of the detected pathways.

Transition path sampling study of the conformational fluctuation of His-64 in human carbonic anhydrase II.

We report here a transition path sampling study of the conformational fluctuation of His-64 that is known to be important in the enzymatic catalysis of human carbonic anhydrase II. The dynamical transition between experimentally detected conformations of His-64 could not be observed using classical molecular dynamics trajectories extended to 3.5 ns, indicating the transition to be rare on the time scale of molecular dynamics. Using the transition path sampling method, an ensemble of transition paths between these two conformers has been generated and analyzed in detail to identify the mechanism of coupling of His-64 to its neighboring residues during the conformational transition. It is found that both Asn-62 and Tyr-7 may contribute toward retaining the His-64 residue in its outward conformation. Trp-5, on the other hand, shows marked motions at the transition state. The number of water molecules inside a part of the active site cavity and the corresponding cavity volume are also found to vary coupled to the His-64 conformational dynamics.

Proton affinities of some amino acid side chains in a restricted environment.

We investigate the dependence of proton affinity values of the side chains of amino acids such as Asp, Glu, His, Ser, and Thr on confinement in a single-walled carbon nanotube. The proton affinity values, estimated using the density functional theories (PW91/dnp and BLYP/dnp), are found to be highly sensitive toward confinement. We find that for both Asp and Glu, the proton affinity, while suspended inside the carbon nanotube, becomes much less in comparison to their respective gas phase values. In the case of His, Ser, and Thr side chains, on the other hand, the proton affinity inside the carbon nanotube becomes negative. Hydrogen bonding with neighboring polar groups is found to result in a marked increase in proton affinity inside the tube in all of the cases reported in this article. The increase is most remarkable in the case of His, Ser, and Thr side chains where the presence of polar neighboring groups within a hydrogen-bonding distance is found to augment the proton affinity value by more than 100 kcal mol(-1).

A theoretical study on the detection of proton transfer pathways in some mutants of human carbonic anhydrase II.

Structural and kinetic studies of mutants can give much insight into the function of an enzyme. We report the detection of possible proton transfer pathways into the active site of a number of mutants of the enzyme human carbonic anhydrase II (HCA II). Using a recently developed method of path search in the protein conformational space, we identify hydrogen-bonded networks (or proton paths) that can dynamically connect the protein surface to the active site through fluctuations in protein structure and hydration. The feasibility of establishing such dynamical connectivities is assessed by computing the change in free energy of conformational fluctuations and compared to those identified earlier in the wild type enzyme. It is found that the point mutation facilitates or suppresses one or more of the alternative pathways. Our results allow the use of a generic set of pathways to correlate qualitatively the residual activity in the mutants to the molecular mechanism of proton transfer in the absence of His at position 64. We also demonstrate how the detected pathways may be used to compare the efficiencies of the mutants His-64-Ala/Asn-62-His and His-64-Ala/Asn-67-His using the empirical valence bond theory.